Yep, it's BeamNG.drive...
This video shows how exactly you have to use the steering to control a motorcycle even without any rider weight to talk about.
First, you initiate a turn with counter-steering. Then, in order to support the bike from toppling over by turning the handlebars inside a tiny bit. That "tiny bit" depends on many parameters and could actually amount to full inside lock in moto-gymkhana-like tight low-speed cornering.
Now, since the sim by default turns the directional control to the straight ahead position when no directional key is pressed (if you use the keyboard), the front wheel won't have enough turn in after leaning over, so that will lead to the bike falling at once. That's why initiating the turn is easy with the keyboard, but preventing it from falling is next to impossible.
I used my G27 instead in this example. Running it at 50° like that as I do in GP Bikes makes it hellishly hard to control the bike, so I had to increase the angle up to around 240°. After giving it some time I can now turn the bike without falling on this flat barren map. Alas, trying to attempt that on actual roads with slopes and cambering might prove impossible.
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